Doctest ignores methods decorated with `functools.singledispatchmethod`

Bug report

Bug description:

Doctest does not recognize tests in the docstrings of methods decorated with functools.singledispatchmethod. There's 2 causes:

1. It checks the dictionary of classes for functions and subclasses, thereby not invoking descriptors. https://github.com/python/cpython/blob/df4a2f5bd74fc582d99e6a82e070058d7765f44d/Lib/doctest.py#L1061-L1073
2. functools.singledispatchmethod does not call functools.update_wrapper on its instance, only on the wrapper function returned from its __get__ method.

A similar issue for cached_property was fixed in #107996.

Example

# mwe.py
import functools

class Class:
    @functools.singledispatchmethod
    def singledispatchmethod(self, arg):
        """
        >>> print(Class().singledispatchmethod(5))
        foo
        """
        return "foo"

    def regularmethod(self, arg):
        """
        >>> print(Class().regularmethod(5))
        foo
        """
        return "foo"

$ python3 -m doctest -v mwe.py
Trying:
    print(Class().regularmethod(5))
Expecting:
    foo
ok
2 items had no tests:
    mwe
    mwe.Class
1 item passed all tests:
   1 test in mwe.Class.regularmethod
1 test in 3 items.
1 passed.
Test passed.

doctest only finds one doctest, where there should be two.

CPython versions tested on:

CPython main branch

Operating systems tested on:

Linux

Linked PRs

• gh-129579

Start in Lib/doctest.py at the class-dictionary handling around lines 1061-1073, then inspect functools.singledispatchmethod and the cached_property fix referenced in issue #107996. Add regression coverage for the example's singledispatchmethod docstring and verify doctest discovers both methods.